A panoply of Schwinger-Keldysh transport

TL;DR

This paper develops a Schwinger-Keldysh effective action for relativistic hydrodynamics in a statistical mechanical limit and shows that microscopic unitarity imposes a new Schwinger-Keldysh positivity constraint beyond the usual second-law and Onsager constraints. By encoding doubled degrees of freedom, KMS symmetry, and a worldvolume formulation with superspace, the authors derive a general action S_eff whose transport content can be classified into scalar terms, non-dissipative tensor terms, dissipative terms, pseudo-dissipative terms, and exceptional terms, with anomaly-induced transport discussed separately. They demonstrate how the ideal fluid arises and how the entropy current is obtained from the action, and provide explicit classifications and examples (including parity-violating 2+1D and second-order neutral fluids) that reveal new unitarity-based restrictions on transport coefficients beyond traditional hydrodynamic criteria. The framework thus links unitarity, KMS structure, and CPT properties to concrete transport coefficients, offering a principled path to understand and constrain hydrodynamic behavior in a wide range of systems and potentially guiding holographic interpretations.

Abstract

We classify all possible allowed constitutive relations of relativistic fluids in a statistical mechanical limit using the Schwinger-Keldysh effective action for hydrodynamics. We find that microscopic unitarity enforces genuinely new constraints on the allowed transport coefficients that are invisible in the classical hydrodynamic description; they are not implied by the second law or the Onsager relations. We term these conditions Schwinger-Keldysh positivity and provide explicit examples of the various allowed terms.